Gliederung

In clinical trials the goal may be to establish non-inferiority of a new treatment compared to a standard treatment. We consider a situation where the primary endpoint is quantitative, but the probability of a fatal outcome is non-negligible thus censoring by death may occur if patients die before the quantitative outcome can be determined. Excluding censored patients is likely to introduce bias.

Felker and Maisel [1] have suggested a global rank endpoint for this type of problem. Matsouaka and Betensky [2] provide a formal description for the situation where superiority is to be demonstrated for a quantitative endpoint in the presence of censoring by death. They also derive power and sample size formulae. Without loss of generality, they assume that high values of the quantitative endpoint represent a favourable outcome. Let N the number of patients in the study of whom m patients have died. Then the ranks 1 to m are assigned to those patients who have died, the surviving patients have ranks m +1 to N according to their values of the quantitative endpoint. Using these rank scores, the Mann-Whitney U statistic is computed.

We apply this idea to the non-inferiority situation as described in [3]. Using the fact that the Mann-Whitney U statistic follows an asymptotically normal distribution and applying the Matsouaka and Betensky formulas for mean and variance of the U statistic, we derived a formula for the power of the Wilcoxon–Mann–Whitney test for non-inferiority in the presence of death-censored observations.

We present an application to planning a study in pulmonary embolism and assess the precision of the formula in a simulation study.